Many of the fundamental optical and electronic properties of atomically thin transition metal dichalcogenides are dominated by strong Coulomb interactions between electrons and holes, forming tightly bound atom-like states called excitons. Here, we directly trace the ultrafast formation of excitons by monitoring the absolute densities of bound and unbound electron-hole pairs in single monolayers of WSe₂ on a diamond substrate following femtosecond nonresonant optical excitation. To this end, phase-locked mid-infrared probe pulses and field-sensitive electro-optic sampling are used to map out the full complex-valued optical conductivity of the nonequilibrium system and to discern the hallmark low-energy responses of bound and unbound pairs. While the spectral shape of the infrared response immediately after above-bandgap injection is dominated by free charge carriers, up to 60% of the electron-hole pairs are bound into excitons already on a subpicosecond time scale, evidencing extremely fast and efficient exciton formation. During the subsequent recombination phase, we still find a large density of free carriers in addition to excitons, indicating a nonequilibrium state of the photoexcited electron-hole system.